It's not clear to me the importance of the Ethereum Virtual Machine and why it is used. So it is natural to ask what would happen if EVM didn't exist? or Ethereum didn't use it.
First to get an idea on EVM you may refer this question on what is EVM. And then,
What would happen if the EVM didn't exist?
As I understand,
Since ethereum should provide a platform independent (Otherwise you need to deploy different contracts at different addresses for different platforms?) running environment to execute smart contracts (providing a Turing Complete language to write smart contracts is a main specialty in Ethereum ) , A VM is highly needed. But why not an existing VM is not used? Ethereum has it's on requirements other than just executing a code. This answer requirements needed for the EVM will give a good idea on that. And this comparison with JVM will give a more insight to that.
Highlighting the security aspect Ethereum Virtual machine(EVM) provides the secured run-time environment for the smart contracts in the network. Smart Contracts are open to everyone in the network and anyone in the network is allowed to deploy smart contracts. When a node need execute a smart contract function, the code is run with in the particular node.
These reasons open up a security vulnerability, unless the run-time environment is not controlled. In a worst case scenario, it may lead nodes to be unavailable and ultimately the network to be unavailable. These vulnerabilities are prevented by controlling the run-time environment by the EVM.
Ethereum provides two main services : Money transfer and Smart contracts processing. The first doesn't need a VM but the second does while a smart contract is a piece of code which needs a VM or a compiler to run it. So no VM no ability to write smart contract or advanced programs handling assets or money.
read this post to get more details about why do they creat a new VM instead using an existing one : What was the reason to invent the EVM?
Ether/Tokens will be transferable and even smartcontracts can be achieved without a VM( as seen in blockchains like Stellar). But such are limited to a few basic logical features.
The main reason why Ethereum needs an EVM is to have Turing Complete smartcontracts. i.e the ability to execute any computable piece of code(basically a "virtual CPU")
The virtual machine is just fancy talk for scripting language. If you've studied Bitcoin, you could say that the Script language built in Bitcoin's code is the "Bitcoin Virtual Machine". It just happens that it is not Turing complete, as the Ethereum scripting language is Turing complete and has higher capabilities (albeit at the cost of more complexity).
Here is a perfect and complete answer to your question. The answer was big enough, so I wrote an article instead. I hope that it will help a lot of people.